For a numerical semigroup,we introduce the concept of a fundamental gap with respect to the multiplicity of the semigroup.The semigroup is fully determined by its multiplicity and these gaps. We study the case when a ...For a numerical semigroup,we introduce the concept of a fundamental gap with respect to the multiplicity of the semigroup.The semigroup is fully determined by its multiplicity and these gaps. We study the case when a set of non-negative integers is the set of fundamental gaps with respect to the multiplicity of a numerical semigroup.Numerical semigroups with maximum and minimum number of this kind of gaps are described.展开更多
In this paper we introduce a particular semigroup transform A that fixes the invariants involved in Wilf's conjecture,except the embedding dimension.It also allows one to arrange the set of non-ordinary and non-ir...In this paper we introduce a particular semigroup transform A that fixes the invariants involved in Wilf's conjecture,except the embedding dimension.It also allows one to arrange the set of non-ordinary and non-irreducible numerical semigroups in a family of rooted trees.In addition,we study another transform,having similar features,that has been introduced by Bras-Amorós,and we make a comparison of them.In particular,we study the behavior of the embedding dimension under the action of such transforms,providing some consequences concerning Wilf's conjecture.展开更多
Let I be an interval of positive rational numbers. Then the set S （I） = T ∩ N, where T is the submonoid of （Q0＋, ＋） generated by T, is a numerical semigroup. These numerical semigroups are called proportionally...Let I be an interval of positive rational numbers. Then the set S （I） = T ∩ N, where T is the submonoid of （Q0＋, ＋） generated by T, is a numerical semigroup. These numerical semigroups are called proportionally modular and can be characterized as the set of integer solutions of a Diophantine inequality of the form ax rood b 〈 cx. In this paper we are interested in the study of the maximal intervals I subject to the condition that S （I） has a given multiplicity. We also characterize the numerical semigroups associated with these maximal intervals.展开更多
文摘For a numerical semigroup,we introduce the concept of a fundamental gap with respect to the multiplicity of the semigroup.The semigroup is fully determined by its multiplicity and these gaps. We study the case when a set of non-negative integers is the set of fundamental gaps with respect to the multiplicity of a numerical semigroup.Numerical semigroups with maximum and minimum number of this kind of gaps are described.
文摘In this paper we introduce a particular semigroup transform A that fixes the invariants involved in Wilf's conjecture,except the embedding dimension.It also allows one to arrange the set of non-ordinary and non-irreducible numerical semigroups in a family of rooted trees.In addition,we study another transform,having similar features,that has been introduced by Bras-Amorós,and we make a comparison of them.In particular,we study the behavior of the embedding dimension under the action of such transforms,providing some consequences concerning Wilf's conjecture.
基金supported by the project MTM2004-01446 and FEDER fundssupported by the Luso-Espanhola action HP2004-0056
文摘Let I be an interval of positive rational numbers. Then the set S （I） = T ∩ N, where T is the submonoid of （Q0＋, ＋） generated by T, is a numerical semigroup. These numerical semigroups are called proportionally modular and can be characterized as the set of integer solutions of a Diophantine inequality of the form ax rood b 〈 cx. In this paper we are interested in the study of the maximal intervals I subject to the condition that S （I） has a given multiplicity. We also characterize the numerical semigroups associated with these maximal intervals.
